Multilevel Inverse-Based Factorization Preconditioner for Solving Sparse Linear Systems in Electromagnetics

Authors

  • Yiming Bu 1 Institute of Mathematics and Computer Science, University of Groningen, Groningen, 9712 CP, The Netherlands , 2 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731
  • Bruno Carpentieri School of Science and Technology, Nottingham Trent University, Burton Street, Nottingham NG1 4BU, UK
  • Zhaoli Shen 1 Institute of Mathematics and Computer Science, University of Groningen, Groningen, 9712 CP, The Netherlands , 2 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731
  • Tingzhu Huang School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731 China

Keywords:

Approximate inverse preconditioners, computational electromagnetics, Krylov subspace methods, sparse matrices

Abstract

We introduce an algebraic recursive multilevel approximate inverse-based preconditioner, based on a distributed Schur complement formulation. The proposed preconditioner combines recursive combinatorial algorithms and multilevel mechanisms to maximize sparsity during the factorization.

Downloads

Download data is not yet available.

References

Y. Bu, B. Carpentieri, Z. Shen, and T.-Z. Huang, “A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems,” Applied Numerical Mathematics, vol. 104, pp. 141-157, 2016.

G. Karypis and V. Kumar, “A fast and high quality multilevel scheme for partitioning irregular graphs,” SIAM J. Sci. Comput., vol. 20, pp. 359-392, 1999.

T. Davis, Sparse Matrix Collection, (1994). Available at the URL: http: //www.cise.ufl.edu/ research/sparse/matrices

Y. Saad, Iterative Methods for Sparse Linear Systems. SIAM Publications, 2nd edition, 2003.

Y. Saad and B. Suchomel, “ARMS: An algebraic recursive multilevel solver for general sparse linear systems,” Numer. Linear Algebra Appl., vol. 9, no. 5, pp. 359-378, 2002.

M. Grote and T. Huckle, “Parallel preconditionings with sparse approximate inverses,” SIAM J. Sci. Comput., vol. 18, pp. 838-853, 1997.

M. Bollhoefer, Y. Saad, and O. Schenk, ILUPACK - Preconditioning Software Package, 2010. Available online at the URL: http://ilupack.tu-bs.de.

Downloads

Published

2021-07-25

How to Cite

[1]
Yiming Bu, Bruno Carpentieri, Zhaoli Shen, and Tingzhu Huang, “Multilevel Inverse-Based Factorization Preconditioner for Solving Sparse Linear Systems in Electromagnetics”, ACES Journal, vol. 33, no. 02, pp. 160–163, Jul. 2021.

Issue

2018: Vol 33 Iss 2

Section

General Submission